Finite three-point bending of a fiber-reinforced beam with a step (Q1073612)

Using the theory of ideal fiber-reinforced composite materials, an equilibrium solution was obtained for the finite three-point bending of a beam which has a central step on its bottom surface. The beam is axially reinforced by fibers and simply supported by fixed roller fulcrums. It was found that the exact solution reached by the rule of trial and error is statically and kinematically admissible only for a linear elastic (or quasielastic) shear response. The equilibrium condition of the portion of the beam corresponding to the step edge is reduced to a Fredholm type integral equation of the second kind with respect to the curvature radius of the uppermost fiber.